Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.aazh)

Hypergeometric2F1

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric2F1[a,b,c,z]

Specific values

For rational parameters with denominators 4 and fixed z

For fixed z and a=-17/4, b>=a

For fixed z and a=-17/4, b=23/4

http://functions.wolfram.com/07.23.03.aazh.01

Input Form

Hypergeometric2F1[-(17/4), 23/4, 3, z] == (1/(1091215125 Pi z^2)) (64 (4 (-14586 - 342771 z + 29956950 z^2 - 195507200 z^3 + 451072000 z^4 - 436207616 z^5 + 150994944 z^6) EllipticE[(1/2) (1 - Sqrt[1 - z])] + (29172 (1 + Sqrt[1 - z]) + 7293 (94 + 95 Sqrt[1 - z]) z - 300 (199713 + 85456 Sqrt[1 - z]) z^2 + 51200 (7637 + 2213 Sqrt[1 - z]) z^3 - 1024000 (881 + 160 Sqrt[1 - z]) z^4 + 8388608 (104 + 9 Sqrt[1 - z]) z^5 - 301989888 z^6) EllipticK[(1/2) (1 - Sqrt[1 - z])]))

Standard Form

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MathML Form

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Rule Form

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Date Added to functions.wolfram.com (modification date)

2007-05-02

HypergeometricPFQ[{},{},z]
HypergeometricPFQ[{},{b},z]
HypergeometricPFQ[{a},{},z]
HypergeometricPFQ[{a},{b},z]
HypergeometricPFQ[{a₁},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅},{b₁,b₂,b₃,b₄},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅,a₆},{b₁,b₂,b₃,b₄,b₅},z]
HypergeometricPFQ[{a₁,...,a_p},{b₁,...,b_q},z]